FRACTIONAL OPTIMAL CONTROL OF THE TIME FRACTIONAL DIFFUSION SYSTEM

In this article, we study a problem of fractional distributed optimal control for the time fractional diffusion system evolving in a spatial domain Ω⊂Rn using distributed bounded controls. We minimize a functional constituted of the deviation between the desired derivative and fractional spatial derivative of order α∈(0, 1) and the energy term. We prove the existence of an optimal control solution of the minimization problem. Then, we characterize the control as the solution to an optimality system.